Increased Range Resolution Using Carrier Phase

The accuracy of range and location coordinates of a target are increased consider-ably by measuring the phase offset between the RF carrier of the received signal and the receiver local oscillator, in addition to the code offset measurement dis-cussed above. A phase comparator circuit can measure carrier phase offset to within a small fraction of a cycle, and considering that the signal travels one wavelength during a cycle, the phase measurement gives a resolution of a fraction of a wave-length. At the GPS L1 frequency of 1.575 GHz, for example, the wavelength is 19 cm. If we assume that carrier phase can be measured at an accuracy of within 15°, then the range accuracy will be (15/360)19 = 0.8 cm. This is two orders of magnitude better than the accuracy obtained by measuring spreading code displacement, which is around 2m for a GPS receiver using the precision (P) code.

The problem with realizing the potential accuracy of carrier phase ranging is that the distance between the communicating terminals is much greater than a wavelength and the number of whole wavelengths in that distance is difficult to ascertain. If N_dequals that number of wavelengths and␸equals the phase compari-son result, 0≤␸< 2␲, then, assuming that the receiver local oscillator cycle begins at the epoch of target symbol transmission, the distance to the target is:

d= Nd␭+ ␸

2␲ ␭⁼冉^Nd+2␸␲冊^{␭ (3.31)}

The integer variable N_dis ambiguous as far as the measurement of␸is con-cerned, and so the value of d can be determined only to the degree that the range of possible values of N_dis known.

We have seen previously in this chapter that incoming and local replica code alignment can be determined to within a fraction of a chip. If this accuracy is within a wavelength, then the carrier phase measurement can add considerably to the range resolution. In the hypothetical situation pictured in Figure 3.32, trans-mitted and received code displacement is measured to within one-fifth of a chip.

There are five carrier cycles per chip period, and they are synchronized to chip boundaries. After acquisition and tracking, the time of flight ␶ is found to be between 2.4 to 2.6 chip periods and measured carrier phase is ␸ = 2.5 radians.

N_d = 2.4 × 5 = 12. The estimated distance is, according to (3.31), d = 12␭ + (2.5/2␲)␭= 12.4␭.

Mitchell [9] has suggested a similar method for tracking the distance between satellites, where the chip rate is 300 chips/second and carrier frequency is 12 GHz.

In his example, pinpointing the carrier cycle within a chip is done by making a

τ

τ 0.2 0.4

0.6 0.8 1.0

ϕ One chip Received

code Transmitted code

Figure 3.32 Increased time resolution using carrier phase comparison.

phase difference measurement on a 300-MHz signal using oscillators synchronized to the replica and received codes, instead of using the DLL tracking mechanism.

He shows that the accuracy of this procedure is sufficient to find the correct carrier cycle among the 40 that make up the chip period.

As mentioned, a typical accuracy of a GPS receiver synchronizing the P code is 2m, whereas the wavelength at 1.575 GHz is 19 cm. This leaves a carrier cycle ambiguity of 10 cycles that must be resolved in order to take advantage of the accuracy provided by carrier phase difference measurement. Differential carrier phase positioning methods cancel out various measurement errors and eliminate the carrier cycle ambiguity. A reference receiver, whose position is known precisely and is located within tens of kilometers from the user receiver, makes carrier phase measurements while continuously tracking multiple satellites. These measurements, together with measurements made by the user GPS receiver, are processed to cancel out ambiguities. When satellite tracking is performed over a period of at least 30 minutes, the distance between the reference receiver and the user receiver can be estimated to closer than 1 cm.

3.6 Conclusions

In addition to its interference rejection properties, DSSS is particularly appropriate for distance measurement because it provides a systematic manner, through a closed loop control mechanism, of achieving high resolution from signal bandwidths that are relatively low. For example, the short GPS C/A code can provide an accuracy of 10m with a chip length of 976 ns, equivalent to a distance of 293m. Accuracy is obtained at the expense of processing time, however. While a high-speed system clock is not required for high-accuracy time difference measurements, one should be aware of the fact that TOF or TDOA measurements do require a precise measurement of the beginning of the phase difference process in the DSSS receiver in order to utilize the high-resolution code phase difference estimation.

Noise and multipath are ultimate factors in the accuracy of the range estimation.

Noise can be countered by low DLL loop bandwidth, with the penalty of increased measurement time and susceptibility to disturbance by system dynamics and phase noise. Multipath interference is alleviated by using high spreading code rates and statistical estimation when location is determined by spatially separated base stations.

References

[1] Sklar, B., Digital Communications Fundamentals and Applications, 2nd ed., New York:

McGraw-Hill, 2001.

[2] Dixon, R. C., Spread Spectrum Systems, 2nd ed., New York: John Wiley & Sons, 1984.

[3] GPS Navstar, Global Positioning System Standard Positioning Service Signal Specification, 2nd ed., US Coast Guard Navigation Center, June 2, 1995.

[4] NAVSTAR GPS User Equipment Introduction, Public Release Version, DOD Joint Program Office, September 1996.

[5] Ward, P. W., J. W. Betz, and C. J. Hegarty, ‘‘Satellite Signal Acquisition, Tracking, and Data Demodulation,’’ in Understanding GPS: Principles and Applications, 2nd ed., E. Kaplan and C. Hegarty, (eds.), Norwood, MA: Artech House, 2006, pp. 153–241.

[6] Nicholson, D. L., Spread Spectrum Signal Design, Rockwell, Maryland: Computer Science Press, 1988.

[7] Peterson, R. L., R. E. Ziemer, and D. E. Borth, Introduction to Spread Spectrum Communi-cations, Upper Saddle River, NJ: Prentice-Hall, 1995.

[8] Braasch, M. S., and A. J. Van Dierandonck, ‘‘GPS Receiver Architectures and Measure-ments,’’ Proceedings of the IEEE, Vol. 37, No. 1, January 1999.

[9] Mitchell, G., ‘‘High-Accuracy Ranging Using Spread-Spectrum Technology,’’ 15th Annual AIAA/USU Conference on Small Satellites, Logan, UT, August 13–16, 2001.